Is math invented or discovered?
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27-10-2016, 02:38 AM
RE: Is math invented or discovered?
(26-10-2016 03:39 PM)unknowndevil666 Wrote:  
(20-10-2016 07:24 PM)Bucky Ball Wrote:  Math is learned.
Humans are pattern seeking monkeys.

That doesn't say anything about whether math is discovered or invented. I can learn about the water cycle (discovered) and I can learn about car engines (invented). Your second comment can also go either way. Does "pattern seeking" mean that nature is filled with patterns that we can find or that we find patterns even where there are none, or something else? I feel like you're saying it's invented though.

Don't get too tied up with "inventing". In the final analysis the internal combustion engine is a collection of previous discoveries - some almost certainly accidental - put together over a period of time.

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27-10-2016, 05:46 PM
RE: Is math invented or discovered?
(27-10-2016 12:32 AM)unknowndevil666 Wrote:  
(25-10-2016 07:26 AM)Chas Wrote:  Yes it is, but so what?
Gravity is an inverse square ratio, but so what?
Pi can be calculated to any degree of significance with a Taylor series, but so what?
Why does it seem significant to you?

It's significant because if an "inverse square ratio" is just the product of man-made mathematical convention, it shouldn't exist outside of any man-made problem unless there is some underlying function that extends beyond the specific case. Take language for example:

Any particular language (English, Chinese, etc.) is a tool, a man-made invention. We don't observe letters or symbols of any language in nature. However, there is a underlying, fundamental property of all languages: communication. Communication is not simply a man-made tool. It is used by humans, but we didn't originate it. We also see communication in nature, among other animals. Math is the same way.

That is a non sequitur.

Quote:Particular systems of mathematics, such as geometry, calculus, number theory, can be viewed as the different languages. We have, conventionally, specified these groups. Another convention, we don't see the symbols that we use (1, *, %) in nature. However, like spoken languages, there is an underlying, fundamental property of all mathematical languages. What is it?

They are all invented. Some are useful for modeling reality, others are not.

Quote:I'll call it "relation" for right now. Mathematics shows how things relate to each other. Take any law of physics, F=G(M*m)/r^2 for instance. Newton didn't just create this formula of his own convention, he discovered this relationship between masses and put it into the syntax of our mathematical language, the same way we can communicate real concepts with man-made words in our English language. And "relation" exists in every field of mathematics, it arises from operation on truth values, logically proving theorems from axioms, etc. One might even say that "relation" doesn't just exist in math, but is the math.

How does that explain mathematical systems that do not model any reality?

Quote:What this all means is that if the "inverse square ratio" was something created by humans for specific problems, it should stay within the realm of those problems.

Another non sequitur. The relationship exists, we have both words and maths to describe it.

Quote:The fact that we've found this is embedded in universal law suggests it's a "relation" that exists outside of our own convention.

Yes, the relationship exists. So?

Quote:You also use pi as an example. The significance of pi being able to be calculated in a Taylor series is that it was originally found by using polygons and circles. If pi was created as a tool to solve geometric problems, then what the hell is it doing in calculus or the Gaussian distribution??

Pi was no more created than the inverse square nature of gravity or radiation was.
The ratio of a circle's circumference to its diameter is a fact. But that existence is not mathematics.

Quote:Our languages of mathematics can define pi using C/d, or the integral of a half-circle function, or Euler's formula (like how one can use different languages to communicate anger) but pi means something more than just the way we use it (like how the language in which we communicate anger is not the actual communication itself).

What does pi mean?

Quote:So yes, we have different methods of mathematics (methods of communication, i.e. language) that we create and use as tools, but that isn't the essence of mathematics itself.

Anyway, I have to go to bed. I'm ending it here.

You are confusing mathematics with reality. We create mathematics to, among other things, model reality.

Skepticism is not a position; it is an approach to claims.
Science is not a subject, but a method.
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27-10-2016, 06:18 PM
RE: Is math invented or discovered?
(27-10-2016 05:46 PM)Chas Wrote:  That is a non sequitur.
...
They are all invented. Some are useful for modeling reality, others are not.
...
How does that explain mathematical systems that do not model any reality?
...
Another non sequitur. The relationship exists, we have both words and maths to describe it.
...
Yes, the relationship exists. So?
...
Pi was no more created than the inverse square nature of gravity or radiation was.
The ratio of a circle's circumference to its diameter is a fact. But that existence is not mathematics.
...
What does pi mean?
...
You are confusing mathematics with reality. We create mathematics to, among other things, model reality.

"Nope"
"That's not true, this is true"
"Wut?"
"Nope"
"So?"
"That's not true, this is true"
"Wut?"
"That's not true, this is true"

Sorry, but I don't feel any reason to continue. I will link this article though: What is π?
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27-10-2016, 06:32 PM
RE: Is math invented or discovered?
(27-10-2016 06:18 PM)unknowndevil666 Wrote:  
(27-10-2016 05:46 PM)Chas Wrote:  That is a non sequitur.
...
They are all invented. Some are useful for modeling reality, others are not.
...
How does that explain mathematical systems that do not model any reality?
...
Another non sequitur. The relationship exists, we have both words and maths to describe it.
...
Yes, the relationship exists. So?
...
Pi was no more created than the inverse square nature of gravity or radiation was.
The ratio of a circle's circumference to its diameter is a fact. But that existence is not mathematics.
...
What does pi mean?
...
You are confusing mathematics with reality. We create mathematics to, among other things, model reality.

"Nope"
"That's not true, this is true"
"Wut?"
"Nope"
"So?"
"That's not true, this is true"
"Wut?"
"That's not true, this is true"

Sorry, but I don't feel any reason to continue. I will link this article though: What is π?

Since you have no constructive response, I see no need to continue either. Drinking Beverage

Skepticism is not a position; it is an approach to claims.
Science is not a subject, but a method.
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